Feng Xue

Pareto-based multi-objective differential evolution

Evolutionary multiobjective optimization (EMOO) finds a set of Pareto solutions rather than any single aggregated optimal solution for a multiobjective problem. The purpose is to describe a newly developed evolutionary approach-Pareto-based multiobjective differential evolution (MODE). The concept of differential evolution, which is well-known in the continuous single-objective domain for its fast convergence and adaptive parameter setting, is extended to the multiobjective problem domain. A Pareto-based approach is proposed to implement the differential vectors. A set of benchmark test functions is used to validate this new approach. We compare the computational results with those obtained in the literature, specifically by strength Pareto evolutionary algorithm (SPEA). It is shown that this new approach tends to be more effective in finding the Pareto front in the sense of accuracy and approximate representation of the real Pareto front with comparable efficiency.

Fuzzy Logic Controlled Multi-Objective Differential Evolution

In recent years, multi-objective evolutionary algorithms (MOEA) have generated a large research interest. MOEAs attraction stems from their ability to find a set of Pareto solutions rather than any single, aggregated optimal solution for a multi-objective problem. As for single-objective evolutionary algorithms (SOEA), multi-objective evolutionary algorithms also require parameter tuning to achieve desirable performance. In the literature we can find fuzzy logic controllers (FLCs) applied to online parameter control for SOEA. In this paper, we propose to use a FLC to dynamically adjust the parameters of a particular multi-objective differential evolution (MODE) algorithm. The fuzzy logic controlled multi-objective differential evolution (FLC-MODE) is applied to a suite of benchmark functions. Its results are compared to those obtained by using MODE with constant parameter settings. We show that the FLC-MODE obtains better results in 80% of the testing examples. Given that the benchmarks were synthetic test functions, we designed the FLC using only our understanding of the working mechanism of the MODE, without incorporating any additional problem-specific knowledge. When addressing real-world applications, we expect the FLC to be an excellent way for representing and leveraging their associated heuristic knowledge

Multi-objective differential evolution and its application to enterprise planning

Agility is important to modern enterprises. The effective coordination of large numbers of potential suppliers and manufacturer, demands a scientific methodology rather than just practical experience to make decisions on supply manufacturing planning problems. Particularly in cases where multiple decision objectives are important to process planning, empirical decisions are insufficient. This paper introduces formal methods to solve such multi-objective decision problems involved in general supply manufacturing planning, and specifically describes the extension of differential evolution methods to discrete problem domains. An enterprise planning problem with two objectives-cycle time and cost is used as a principal example. Such multi-objective optimization problems usually are very large and nonlinear. In this paper, the concept of differential evolution, which is well-known in single-objective continuous domain for its fast convergence and adaptive parameter setting, is extended to the discrete domain by introducing greedy probability, mutation probability, and crossover probability. Moreover, this concept is extended to discrete multi-objective optimization problem. The proposed discrete multi-objective differential evolution, or D-MODE algorithm is applied to obtain Pareto solutions of this general planning problem. A practical example in the electronics industry is used as an illustrative example to demonstrate the effectiveness of the proposed D-MODE.

Multiobjective Evolutionary Decision Support for Design–Supplier–Manufacturing Planning

Product development in modern enterprises usually involves collaboration among designers, suppliers, contract manufacturers to achieve efficiency and rapid response to changing markets. Product-development cost, lead time, and reliability are very critical elements in addition to functional features. However, it becomes increasingly challenging to obtain an optimal decision with respect to these multiple criteria as the number of involved entities increases in modern product developments. There is a clear need for planning tools to support effective decision making in this domain. The availability of efficient and accurate multiobjective optimization (MOO) algorithms becomes critical in such a decision support tool. This paper poses the product development as a multiobjective assignment problem in the context of printed circuit board assembly (PCBA) industry. We describe a new class of MOO algorithm based on the principles of differential evolution (DE). The multiobjective DE (MODE) algorithm is shown to approach Pareto-optimal solutions in a wide class of problems with better performance than the nondominated sorting genetic algorithm II from the literature, providing a practical tool for product-development decision support. A decision support system based on the object-oriented design methodology is described in this paper with the MODE as the core search engine. Experimental study of this decision support system is conducted using two real-world PCBA designs. We demonstrate the effectiveness of this proposed MODE algorithm and some use cases of such decision support system on facilitating decision makers tradeoff analysis.

Modeling and convergence analysis of a continuous multi-objective differential evolution algorithm

This paper reports a mathematical modeling and convergence analysis of a continuous multi-objective differential evolution (C-MODE) algorithm that is proposed very recently. This C-MODE is studied in the context of global random search. The convergence of the population to the Pareto optimal solutions with probability one is developed. In order to facilitate the understanding of the C-MODE operators in a continuous space, a mathematical analysis of the operators is conducted based upon a Gaussian distributed initial population. A set of guidelines is derived for the parameter setting of the C-MODE based on the theoretical results from the mathematical analysis. A simulation analysis on a specific numerical example is conducted to validate the mathematical analytical results and parameter-setting guidelines. The performance comparison based on a suite of complex benchmark functions also demonstrates the merits of such parameter-setting guidelines

Multi-objective differential evolution - algorithm, convergence analysis, and applications

The revival of multi-objective optimization (MOO) is mostly due to the recent development of evolutionary multi-objective optimization that allows the generation of the whole Pareto optimal front. Several evolutionary algorithms have been developed for this purpose. This paper focuses on the recent development of differential evolution (DE) algorithms for the multi-objective optimization purposes. Although there are a few other papers on the extension of DE concept to the MOO domain, this paper is intended to provide an overall picture of one specific multi-objective differential evolution (MODE) algorithm. In the MODE, the DE concept for the continuous single-objective optimization is extended to MOO for both continuous and discrete problems (C-MODE and D-MODE, respectively). The MODE is modeled in the context of Markov framework and global random search. Convergence properties are developed for both C-MODE and D-MODE. In particular, a set of parameter-setting guidelines for the C-MODE is derived based on the mathematical analysis. An application of the D-MODE to the planning of design, supply, and manufacturing resources in product development is also reported in this paper

A Review of Two Industrial Deployments of Multi-criteria Decision-making Systems at General Electric

Two industrial deployments of multi-criteria decision-making systems at General Electric are reviewed from the perspective of their multi-criteria decision-making component similarities and differences. The motivation is to present a framework for multi-criteria decision-making system development and deployment. The first deployment is a financial portfolio management system that integrates hybrid multi-objective optimization and interactive Pareto frontier decision-making techniques to optimally allocate financial assets while considering multiple measures of return and risk, and numerous regulatory constraints. The second deployment is a power plant management system that integrates predictive modeling based on neural networks, optimization based on multi-objective evolutionary algorithms, and automated decision-making based on Pareto frontier techniques. The integrated approach, embedded in a real-time plant optimization and control software environment dynamically optimizes emissions and efficiency while simultaneously meeting load demands and other operational constraints in a complex real-world power plant